You'll need to ask the guy who came up with the concept of REST, Roy Fielding, or read his published thesis that forms the description of REST with respect to the web.
Its probably best to start at the top and work your way through it.
What do we transfer - a representation of the resource.
In short, we don't transfer an actual object but a representation of it in some form (eg a html table to represent a database table).
A relevant quote is:
Depending on the message control data, a given representation may
indicate the current state of the requested resource, the desired
state for the requested resource, or the value of some other resource,
such as a representation of the input data within a client's query
form, or a representation of some error condition for a response. For
example, remote authoring of a resource requires that the author send
a representation to the server, thus establishing a value for that
resource that can be retrieved by later requests.